Finite Group Databasebeta

C23×C22⋊(C67⋊C8) #31719258

order17152
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊(C67⋊C8)

Splittings

SylowC67 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D67
commutatorC2×C67C24×C8
FrattiniC2×C4C24×D67
FittingC25×C4×C67C2
socleC25×C67C2×C4
prime radicalC26×C67C4
cosocleC2×C4×C67C25
hypercenterC25×C4D67
hypocenterC67C23×C22⋊C8
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C24×C4 ◁ C25×C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

4384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1032995);