Finite Group Databasebeta

#1976×D67 #30859801

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#1976×D67

Splittings

FittingC67×#1976 ⋊ C2
SylowC67 ⋊ C2×#1976

Subgroups

subgroupG/H
centerC4#121×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC67×#1976C2
socleC2×C67C2×#390
prime radicalC2×#135×D67C2
cosocleC22×C4×C67C24
hypercenter#1976D67
hypocenterC67C2×#1976
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1976

1474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 173538);