Finite Group Databasebeta

#1477×D67 #30822195

order17152
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct product#1477×D67

Splittings

FittingC67×#1477 ⋊ C2
SylowC67 ⋊ C2×#1477

Subgroups

subgroupG/H
centerC2×C4C2×D4×D67
commutatorC4×C67C23×C8
FrattiniC42C23×D67
FittingC67×#1477C2
socleC22×C67C22×C22⋊C4
prime radicalC2×#41×D67C4
cosocleC42×C67C24
hypercenter#1477D67
hypocenterC67C2×#1477
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

1370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 135932);