Finite Group Databasebeta

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C5×C7×C11×Dic21 #44568525

order32340
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C11×Dic21
unambiguous semidirect productC3⋊(C5×C7×C11×Dic7)
unambiguous semidirect productC7⋊(C5×C7×C11×Dic3)

Splittings

derivedC3×C7 ⋊ C4×C5×C7×C11
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ Dic3
HallC3×C72×C11 ⋊ C4×C5
HallC3×C5×C72 ⋊ C4×C11
HallC72×C11 ⋊ C5×Dic3
HallC5×C72 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ C7×Dic7
HallC3×C72 ⋊ C4×C5×C11
SylowC72 ⋊ C5×C11×Dic3
HallC3×C11 ⋊ C5×C7×Dic7
HallC3×C5 ⋊ C7×C11×Dic7
SylowC3 ⋊ C5×C7×C11×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C11D21
commutator, hypocenterC3×C7C4×C5×C7×C11
FrattiniC2C5×C7×C11×D21
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C3×C7C2×C5×C7×C11
LCSG ▷ C3×C7
UCSC1 ◁ C2×C5×C7×C11

144 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

9240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 227);