Finite Group Databasebeta

#1684×D67 #30838227

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

Aliases

direct product#1684×D67

Splittings

FittingC67×#1684 ⋊ C2
SylowC67 ⋊ C2×#1684

Subgroups

subgroupG/H
centerC22#121×D67
commutator, cosocleC42×C67C24
FrattiniC42C23×D67
FittingC67×#1684C2
socleC22×C67C2×#121
prime radicalC22×D67#121
hypercenter#1684D67
hypocenterC67C2×#1684
LCSG ▷ C42×C67 ▷ C22×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ #1684

638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 151964);