Finite Group Databasebeta

C2×Dic3824 #44486853

order30592
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic3824

Splittings

SylowC239 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22D3824
commutator, cosocleC16×C239C23
FrattiniC16C22×D239
FittingC2×C32×C239C2
socle, prime radicalC22×C239D16
hypercenterC2×C32D239
hypocenterC239C2×Q64
LCSG ▷ C16×C239 ▷ C8×C239 ▷ C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30592

Conjugacy classes & character table

7654 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 6815);