Finite Group Databasebeta

C2×#22580876 #31809625

order17792
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22580876

Splittings

SylowC139 ⋊ C2×#396

Subgroups

subgroupG/H
centerC24C22×D139
commutator, cosocleC23×C139C24
FrattiniC23C23×D139
FittingC22×C22⋊C4×C139C2
socleC24×C139C23
prime radicalC25×C139C22
hypercenterC22×C22⋊C4D139
hypocenterC139C2×#396
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C24 ◁ C22×C22⋊C4

908 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8896

Conjugacy classes & character table

2804 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 7731);