Finite Group Databasebeta

C2×#27131248 #37565221

order24256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27131248

Splittings

SylowC379 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic379
commutatorC22×C379C22×C4
FrattiniC2×C4C22×D379
Fitting, prime radicalC22×D4×C379C2
socleC22×C379C22⋊C4
cosocleC2×C4×C379C23
hypercenterC22×D4D379
hypocenterC379C2×#100
LCSG ▷ C22×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6064

Conjugacy classes & character table

3802 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 526);