Finite Group Databasebeta

#2025×D67 #30883103

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

Aliases

direct product#2025×D67

Splittings

FittingC67×#2025 ⋊ C2
SylowC67 ⋊ C2×#2025

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC22×C4×C67C24
FrattiniC22×C4C23×D67
FittingC67×#2025C2
socleC23×C67C22×D4
prime radicalC22×D4×D67C22
hypercenter#2025D67
hypocenterC67C2×#2025
LCSG ▷ C22×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2025

1518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 196840);