Finite Group Databasebeta

C2×#22561496 #30883686

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22561496

Splittings

FittingC2×#423×C67 ⋊ C2
SylowC67 ⋊ C2×#2050

Subgroups

subgroupG/H
centerC2×C4#14524032
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#423×C67C2
socleC22×C67#394
prime radicalC2×#16864196C2
hypercenterC2×#423D67
hypocenterC67C2×#2050
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#423

1382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 197423);