Finite Group Databasebeta

C2×#27163784 #38768579

order25472
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27163784

Splittings

SylowC199 ⋊ C2×#342

Subgroups

subgroupG/H
centerC23(C2×D199)⋊C4
commutatorC22×C199C2×C42
FrattiniC24C22×D199
FittingC22×C22⋊C4×C199C2
socleC23×C199C22⋊C4
prime radicalC25×C199C22
cosocleC24×C199C23
hypercenterC22×C22⋊C4D199
hypocenterC199C2×#342
LCSG ▷ C22×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

680 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, 4239);