Finite Group Databasebeta

C2×Dic3076 #37589917

order24608
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic3076

Splittings

SylowC769 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22D3076
commutator, cosocleC4×C769C23
FrattiniC4C22×D769
FittingC2×C8×C769C2
socle, prime radicalC22×C769D4
hypercenterC2×C8D769
hypocenterC769C2×Q16
LCSG ▷ C4×C769 ▷ C2×C769 ▷ C769
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24608

Conjugacy classes & character table

6158 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24608, 164);