Finite Group Databasebeta

#2072×D67 #30884571

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#2072×D67

Splittings

FittingC67×#2072 ⋊ C2
SylowC67 ⋊ C2×#2072

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC67×#2072C2
socleC23×C67C22×D4
prime radicalC23×D67C2×D4
hypercenter#2072D67
hypocenterC67C2×#2072
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2072

1150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 198308);