Finite Group Databasebeta

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C4×C7×C127⋊C7 #38733525

order24892
automorphism?
homologyAbelianization (H1) = C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC4×C7×C127⋊C7
unambiguous semidirect product(C4×C127)⋊C72
unambiguous semidirect product(C4×C7×C127)⋊C7

Splittings

FittingC4×C7×C127 ⋊ C7
derived, SylowC127 ⋊ C4×C72
HallC4×C127 ⋊ C72

Subgroups

subgroupG/H
center, hypercenterC4×C7C127⋊C7
commutator, hypocenterC127C4×C72
FrattiniC2C2×C7×C127⋊C7
FittingC4×C7×C127C7
socleC2×C7×C127C2×C7
prime radicalC2×C7×C127⋊C7C2
cosocleC2×C127C2×C72
LCSG ▷ C127
UCSC1 ◁ C4×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3556

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24892, 18);