Finite Group Databasebeta

C2×Q16×C71⋊C8 #31966823

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

Aliases

direct productC2×Q16×C71⋊C8

Splittings

SylowC71 ⋊ C2×C8×Q16

Subgroups

subgroupG/H
centerC22×C4D4×D71
commutatorC4×C71C23×C8
FrattiniC42C23×D71
FittingC2×C4×Q16×C71C2
socle, prime radicalC23×C71C4×D4
cosocleC42×C71C24
hypercenterC2×C4×Q16D71
hypocenterC71C2×C8×Q16
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 138939);