Finite Group Databasebeta

C2×#27131252 #37565231

order24256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27131252

Splittings

SylowC379 ⋊ C2×#102

Subgroups

subgroupG/H
centerC23C22⋊D379
commutatorC4×C379C22×C4
FrattiniC2×C4C22×D379
Fitting, prime radicalC22×D4×C379C2
socleC23×C379D4
cosocleC2×C4×C379C23
hypercenterC22×D4D379
hypocenterC379C2×#102
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12128

Conjugacy classes & character table

3808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 536);