Finite Group Databasebeta

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2−1+4×C71⋊C8 #32863489

order18176
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×C71⋊C8

Splittings

SylowC71 ⋊ C8×2−1+4

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D71
commutatorC2×C71C24×C8
FittingC4×2−1+4×C71C2
socleC22×C71C24×C4
prime radicalC2×2−1+4×C71C4
cosocleC2×C4×C71C25
hypercenterC4×2−1+4D71
hypocenterC71C8×2−1+4
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

2190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1035605);