Finite Group Databasebeta

C2×#27163774 #38768550

order25472
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#27163774

Splittings

SylowC199 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×Dic199
commutatorC4×C199C2×C42
FrattiniC22×C4C22×D199
FittingC2×#117×C199C2
socleC22×C199#95
prime radicalC24×C199D4
cosocleC22×C4×C199C23
hypercenterC2×#117D199
hypocenterC199C2×H(3,ℤ/4)
LCSG ▷ C4×C199 ▷ C199
UCSC1 ◁ C2×C4 ◁ C2×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6368

Conjugacy classes & character table

4004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 4210);