Finite Group Databasebeta

C2×Dic3032 #37565672

order24256
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic3032

Splittings

SylowC379 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D3032
commutator, cosocleC8×C379C23
FrattiniC8C22×D379
FittingC2×C16×C379C2
socle, prime radicalC22×C379D8
hypercenterC2×C16D379
hypocenterC379C2×Q32
LCSG ▷ C8×C379 ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24256

Conjugacy classes & character table

6070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 977);