Finite Group Databasebeta

C2×Dic3056 #37574825

order24448
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic3056

Splittings

SylowC191 ⋊ C2×Q64

Subgroups

subgroupG/H
centerC22D3056
commutator, cosocleC16×C191C23
FrattiniC16C22×D191
FittingC2×C32×C191C2
socle, prime radicalC22×C191D16
hypercenterC2×C32D191
hypocenterC191C2×Q64
LCSG ▷ C16×C191 ▷ C8×C191 ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

Conjugacy classes & character table

6118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6815);