Finite Group Databasebeta

C2×Dic3064 #37588779

order24512
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic3064

Splittings

SylowC383 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22D3064
commutator, cosocleC8×C383C23
FrattiniC8C22×D383
FittingC2×C16×C383C2
socle, prime radicalC22×C383D8
hypercenterC2×C16D383
hypocenterC383C2×Q32
LCSG ▷ C8×C383 ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24512

Conjugacy classes & character table

6134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24512, 977);