Finite Group Databasebeta

C2×#120×Dic67 #31014246

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

Aliases

direct productC2×#120×Dic67

Splittings

SylowC67 ⋊ C2×C4×#120

Subgroups

subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
Fitting, prime radicalC22×#120×C67C2
socleC24×C67C24
cosocleC23×C67C25
hypercenterC22×#120D67
hypocenterC67C2×C4×#120
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×#120

8582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 327983);