Finite Group Databasebeta

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C3×C5×C7×C11×Dic7 #44568537

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×C11×Dic7

Splittings

derivedC7 ⋊ C3×C4×C5×C7×C11
HallC3×C5×C72×C11 ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ C4×C5
HallC3×C5×C72 ⋊ C4×C11
HallC72×C11 ⋊ C3×C4×C5
HallC5×C72 ⋊ C3×C4×C11
HallC3×C72 ⋊ C4×C5×C11
SylowC72 ⋊ C3×C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7×C11D7
commutator, hypocenterC7C3×C4×C5×C7×C11
FrattiniC2C3×C5×C7×C11×D7
Fitting, socle, prime radicalC2×C3×C5×C72×C11C2
cosocleC2×C7C2×C3×C5×C7×C11
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C7×C11

144 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 80 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

11550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 239);