Finite Group Databasebeta

C2×#27163782 #38768573

order25472
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27163782

Splittings

SylowC199 ⋊ C2×#341

Subgroups

subgroupG/H
centerC22×C4C22⋊D199
commutatorC4×C199C2×C42
FrattiniC22×C4C22×D199
FittingC22×M16×C199C2
socleC23×C199C4⋊C4
prime radicalC24×C199Q8
cosocleC22×C4×C199C23
hypercenterC22×M16D199
hypocenterC199C2×#341
LCSG ▷ C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12736

Conjugacy classes & character table

4016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25472, 4233);