Finite Group Databasebeta

C2×#27160463 #38737980

order25184
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27160463

Splittings

FittingC2×Q8×C787 ⋊ C2
SylowC787 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D787
commutator, cosocleC4×C787C23
FrattiniC4C22×D787
FittingC2×Q8×C787C2
socleC22×C787D4
prime radicalC2×D3148C2
hypercenterC2×Q8D787
hypocenterC787C2×SD16
LCSG ▷ C4×C787 ▷ C2×C787 ▷ C787
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12592

Conjugacy classes & character table

3944 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25184, 159);