Finite Group Databasebeta

#1879×D67 #30857151

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct product#1879×D67

Splittings

FittingC67×#1879 ⋊ C2
SylowC67 ⋊ C2×#1879

Subgroups

subgroupG/H
centerC23C2×D4×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC67×#1879C2
socleC23×C67C22×D4
prime radicalC22×D8×D67C2
cosocleC22×C4×C67C24
hypercenter#1879D67
hypocenterC67C2×#1879
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

2470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 170888);