Finite Group Databasebeta

C42×C4⋊Dic67 #30776910

order17152
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43

Aliases

direct productC42×C4⋊Dic67

Splittings

SylowC67 ⋊ C42×C4⋊C4

Subgroups

subgroupG/H
centerC22×C42C2×D67
commutatorC2×C67C2×C43
FrattiniC24C23×D67
FittingC2×C43×C67C2
socle, prime radical, cosocleC24×C67C24
hypercenterC2×C43D67
hypocenterC67C42×C4⋊C4
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C42 ◁ C2×C43

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

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, 90647);