Finite Group Databasebeta

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C107×Dic63 #41004059

order26964
automorphism?
homologyAbelianization (H1) = C4×C107 · Schur multiplier (H2) = C1

Aliases

direct productC107×Dic63
unambiguous semidirect productC7⋊(Dic9×C107)
unambiguous semidirect productC9⋊(Dic7×C107)

Splittings

derived, HallC7×C9 ⋊ C4×C107
HallC7×C9×C107 ⋊ C4
HallC9×C107 ⋊ Dic7
HallC7×C107 ⋊ Dic9
SylowC9 ⋊ Dic7×C107
SylowC7 ⋊ Dic9×C107

Subgroups

subgroupG/H
center, hypercenterC2×C107D63
commutator, hypocenterC7×C9C4×C107
FrattiniC2×C3D21×C107
FittingC2×C7×C9×C107C2
socle, prime radicalC2×C3×C7×C107D3
cosocleC2×C7×C9C2×C107
LCSG ▷ C7×C9
UCSC1 ◁ C2×C107

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26964

Conjugacy classes & character table

7062 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26964, 8);