Finite Group Databasebeta

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C4×#20259348 #37581328

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#20259348

Splittings

FittingC2×C4×D4×C191 ⋊ C2
SylowC191 ⋊ C4×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
FittingC2×C4×D4×C191C2
socleC22×C191C22×D4
prime radicalC2×#20259348C2
cosocleC2×C4×C191C24
hypercenterC2×C4×D4D191
hypocenterC191C4×AGL(1,ℤ/8)
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

548 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6112

Conjugacy classes & character table

3844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13318);