Finite Group Databasebeta

#1292×D67 #30745773

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#1292×D67

Splittings

FittingC67×#1292 ⋊ C2
SylowC67 ⋊ C2×#1292

Subgroups

subgroupG/H
centerC22#95×D67
commutatorC2×C4×C67C2×C42
FrattiniC2×C42C22×D67
FittingC67×#1292C2
socleC22×C67C2×#95
prime radicalC23×D67C4⋊C4
cosocleC2×C42×C67C23
hypercenter#1292D67
hypocenterC67C2×#1292
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

690 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, 59510);