Finite Group Databasebeta

#1381×D67 #30770716

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

Aliases

direct product#1381×D67

Splittings

FittingC67×#1381 ⋊ C2
SylowC67 ⋊ C2×#1381

Subgroups

subgroupG/H
centerC2×C4D8×D67
commutatorC8×C67C2×C42
FrattiniC22×C8C22×D67
FittingC67×#1381C2
socleC22×C67C2×#107
prime radicalC23×D67Q16
cosocleC22×C8×C67C23
hypercenter#1381D67
hypocenterC67C2×#1381
LCSG ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1381

574 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, 84453);