Finite Group Databasebeta

← Prev (#32156754) Next (#32156756) →

C2×Q8×C4⋊Dic71 #32156755

order18176
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q8×C4⋊Dic71

Splittings

SylowC71 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC22×C4×Q8×C71C2
socle, prime radicalC24×C71C24
cosocleC23×C71C25
hypercenterC22×C4×Q8D71
hypocenterC71C2×Q8×C4⋊C4
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C4×Q8

3246 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, 328871);