Finite Group Databasebeta

C2×C4×C22⋊C4×D67 #31014002

order17152
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC2×C4×C22⋊C4×D67

Splittings

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

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC2×C67C23×C42
FrattiniC23C24×D67
FittingC2×C4×C22⋊C4×C67C2
socleC24×C67C24
prime radicalC25×D67C22
cosocleC23×C67C25
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C22×C4×C22⋊C4
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

9534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 327739);