Finite Group Databasebeta

C4×#20259258 #37572422

order24448
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#20259258

Splittings

SylowC191 ⋊ C4×#108

Subgroups

subgroupG/H
centerC42D764
commutatorC4×C191C2×C42
FrattiniC22×C4C22×D191
FittingC2×C4×C8×C191C2
socleC22×C191C2×C4⋊C4
prime radicalC23×C191C2×Q8
cosocleC22×C4×C191C23
hypercenterC2×C4×C8D191
hypocenterC191C4×#108
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

6136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 4412);