Finite Group Databasebeta

C2×#22569035 #31719922

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#22569035

Splittings

FittingC22×#102×C67 ⋊ C2
SylowC67 ⋊ C2×#2946

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC22×#102×C67C2
socleC23×C67C22×D4
prime radicalC22×#14524069C2
cosocleC2×C4×C67C25
hypercenterC22×#102D67
hypocenterC67C2×#2946
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#102

2946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1936 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033659);