Finite Group Databasebeta

C2×#22561783 #30885795

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

Aliases

direct productC2×#22561783

Splittings

SylowC67 ⋊ C2×#2102

Subgroups

subgroupG/H
centerC2×C4#14524030
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC2×#430×C67C2
socleC22×C67#400
prime radicalC24×C67#41
hypercenterC2×#430D67
hypocenterC67C2×#2102
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#430

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1504 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 199532);