Finite Group Databasebeta

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C7×Dic7×C121 #37557349

order23716
automorphism?
homologyAbelianization (H1) = C4×C7×C121 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic7×C121
unambiguous semidirect productC7⋊(C4×C7×C121)

Splittings

derivedC7 ⋊ C4×C7×C121
HallC72×C121 ⋊ C4
SylowC72 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC2×C7×C121D7
commutator, hypocenterC7C4×C7×C121
FrattiniC2×C11C7×C11×D7
FittingC2×C72×C121C2
socle, prime radicalC2×C72×C11C2×C11
cosocleC2×C7×C11C2×C7×C11
LCSG ▷ C7
UCSC1 ◁ C2×C7×C121

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3388

Conjugacy classes & character table

8470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23716, 12);