Finite Group Databasebeta

C2×#27132514 #37574854

order24448
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×#27132514

Splittings

SylowC191 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×D191
commutatorC2×C191C22×C42
FrattiniC23C23×D191
FittingC2×#95×C191C2
socle, prime radicalC24×C191C23
cosocleC23×C191C24
hypercenterC2×#95D191
hypocenterC191C2×C4×C4⋊C4
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C24 ◁ C2×#95

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

Conjugacy classes & character table

3880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6844);