Finite Group Databasebeta

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C4⋊C8×Dic142 #32016245

order18176
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C8×Dic142

Splittings

SylowC71 ⋊ Q8×C4⋊C8

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC4×C4⋊C8×C71C2
socle, prime radicalC23×C71C23×C4
cosocleC22×C4×C71C24
hypercenterC4×C4⋊C8D71
hypocenterC71Q8×C4⋊C8
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C8

896 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 188361);