Finite Group Databasebeta

C2×#22560662 #30857612

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#22560662

Splittings

FittingC23×C22⋊C4×C67 ⋊ C2
SylowC67 ⋊ C2×#1898

Subgroups

subgroupG/H
centerC23C2×(C2×D67)⋊C4
commutatorC23×C67C23×C4
FrattiniC24C23×D67
FittingC23×C22⋊C4×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC22×#14524012C2
cosocleC24×C67C24
hypercenterC23×C22⋊C4D67
hypocenterC67C2×#1898
LCSG ▷ C23×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C26 ◁ C23×C22⋊C4

3746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

2704 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 171349);