Finite Group Databasebeta

C2×#22559554 #30838148

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

Aliases

direct productC2×#22559554

Splittings

SylowC67 ⋊ C2×#1666

Subgroups

subgroupG/H
centerC23#14524014
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC2×#492×C67C2
socleC23×C67#121
prime radicalC2×#127×C67C22
hypercenterC2×#492D67
hypocenterC67C2×#1666
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 151885);