Finite Group Databasebeta

C2×#124×Dic67 #31014305

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#124×Dic67

Splittings

SylowC67 ⋊ C2×C4×#124

Subgroups

subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC22×#124×C67C2
socleC24×C67C24
prime radicalC23×D4×C67C22
cosocleC23×C67C25
hypercenterC22×#124D67
hypocenterC67C2×C4×#124
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×#124

3790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 328042);