Finite Group Databasebeta

C2×#22560652 #30857584

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#22560652

Splittings

FittingC23×C42×C67 ⋊ C2
SylowC67 ⋊ C2×#1896

Subgroups

subgroupG/H
centerC22×C4C2×D268
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC23×C42×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC2×#16863907C2
cosocleC22×C4×C67C24
hypercenterC23×C42D67
hypocenterC67C2×#1896
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×C42

2514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

4312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 171321);