Finite Group Databasebeta

C2×#22559546 #30837002

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22559546

Splittings

SylowC67 ⋊ C2×#1664

Subgroups

subgroupG/H
centerC23#14524013
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC2×#329×C67C2
socleC23×C67#120
prime radicalC22×D4×C67D4
hypercenterC2×#329D67
hypocenterC67C2×#1664
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1294 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 150739);