Finite Group Databasebeta

C22⋊C4×(C2×D67)⋊C4 #30777231

order17152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22⋊C4×(C2×D67)⋊C4

Splittings

FittingC2×C4×C22⋊C4×C67 ⋊ C2
SylowC67 ⋊ C22⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D67
commutatorC22×C67C22×C42
FittingC2×C4×C22⋊C4×C67C2
socle, cosocleC24×C67C24
prime radicalC25×D67C22
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C22⋊C42
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

4254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 90968);