Finite Group Databasebeta

C2×Dic3704 #44445221

order29632
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic3704

Splittings

SylowC463 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D3704
commutator, cosocleC8×C463C23
FrattiniC8C22×D463
FittingC2×C16×C463C2
socle, prime radicalC22×C463D8
hypercenterC2×C16D463
hypocenterC463C2×Q32
LCSG ▷ C8×C463 ▷ C4×C463 ▷ C2×C463 ▷ C463
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29632

Conjugacy classes & character table

7414 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29632, 977);