Finite Group Databasebeta

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C8×#14556093 #31996057

order18176
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC8×#14556093

Splittings

SylowC71 ⋊ C4×C8×Q8

Subgroups

subgroupG/H
centerC22×C8C22×D71
commutatorC2×C71C22×C4×C8
FrattiniC22×C4C23×D71
FittingC8×C4⋊C4×C71C2
socle, prime radicalC23×C71C23×C4
cosocleC22×C4×C71C24
hypercenterC8×C4⋊C4D71
hypocenterC71C4×C8×Q8
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C8 ◁ C8×C4⋊C4

1070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 168173);