Finite Group Databasebeta

C2×#22592175 #32165491

order18176
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22592175

Splittings

SylowC71 ⋊ C2×#2451

Subgroups

subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C4⋊Q8×C71C2
socle, prime radicalC24×C71C24
hypercenterC22×C4⋊Q8D71
hypocenterC71C2×#2451
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

2702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 337607);