Finite Group Databasebeta

#2026×D67 #30883115

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#2026×D67

Splittings

FittingC67×#2026 ⋊ C2
SylowC67 ⋊ C2×#2026

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC67×#2026C2
socleC23×C67C22×D4
prime radicalC23×D67C2×D4
hypercenter#2026D67
hypocenterC67C2×#2026
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2026

1302 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, 196852);