Finite Group Databasebeta

C2×#22562548 #31014014

order17152
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×#22562548

Splittings

FittingC2×#376×C67 ⋊ C2
SylowC67 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC2×C67C23×C42
FrattiniC23C24×D67
FittingC2×#376×C67C2
socleC24×C67C24
prime radicalC24×D67C23
cosocleC23×C67C25
hypercenterC2×#376D67
hypocenterC67C2×C4×#117
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×#376

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 327751);