Finite Group Databasebeta

C22×C22⋊C8×D67 #31719256

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

Aliases

direct productC22×C22⋊C8×D67

Splittings

FittingC22×C22⋊C8×C67 ⋊ C2
SylowC67 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC2×C67C24×C8
FrattiniC2×C4C24×D67
FittingC22×C22⋊C8×C67C2
socleC24×C67C22×C4
prime radicalC25×D67C4
cosocleC2×C4×C67C25
hypercenterC22×C22⋊C8D67
hypocenterC67C23×C22⋊C8
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C22⋊C8

7646 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, 1032993);