Finite Group Databasebeta

C2×#27132405 #37571104

order24448
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27132405

Splittings

SylowC191 ⋊ C2×#330

Subgroups

subgroupG/H
centerC23C22⋊Dic191
commutatorC2×C4×C191C22×C4
FrattiniC42C22×D191
FittingC2×#125×C191C2
socle, prime radicalC23×C191C22⋊C4
cosocleC42×C191C23
hypercenterC2×#125D191
hypocenterC191C2×#330
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

Conjugacy classes & character table

2698 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 3094);