Finite Group Databasebeta

C2×Q8×C71⋊C16 #32150934

order18176
automorphism?
homologyAbelianization (H1) = C23×C16 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×C71⋊C16

Splittings

SylowC71 ⋊ C2×Q8×C16

Subgroups

subgroupG/H
centerC22×C8C22×D71
commutatorC2×C71C23×C16
FrattiniC2×C8C23×D71
FittingC2×C8×Q8×C71C2
socle, prime radicalC23×C71C22×C8
cosocleC2×C8×C71C24
hypercenterC2×C8×Q8D71
hypocenterC71C2×Q8×C16
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

582 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, 323050);