Finite Group Databasebeta

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C3×C5×C7×C11×Dic5 #37528404

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C7×C11×Dic5

Splittings

derivedC5 ⋊ C3×C4×C5×C7×C11
HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC3×C52×C11 ⋊ C4×C7
HallC3×C52×C7 ⋊ C4×C11
HallC52×C11 ⋊ C3×C4×C7
HallC52×C7 ⋊ C3×C4×C11
HallC3×C52 ⋊ C4×C7×C11
SylowC52 ⋊ C3×C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7×C11D5
commutator, hypocenterC5C3×C4×C5×C7×C11
FrattiniC2C3×C5×C7×D5×C11
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C5C2×C3×C5×C7×C11
LCSG ▷ C5
UCSC1 ◁ C2×C3×C5×C7×C11

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

normal subgroups only

This group has 128 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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 215);