Finite Group Databasebeta

C2×D4×(C2×D67)⋊C4 #31015000

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×D4×(C2×D67)⋊C4

Splittings

FittingC22×C4×D4×C67 ⋊ C2
SylowC67 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC22×C4×D4×C67C2
socleC24×C67C24
prime radicalC23×D4×D67C2
cosocleC23×C67C25
hypercenterC22×C4×D4D67
hypocenterC67C2×D4×C22⋊C4
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C4×D4

8774 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, 328737);