Finite Group Databasebeta

#1387×D67 #30770752

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

Aliases

direct product#1387×D67

Splittings

FittingC67×#1387 ⋊ C2
SylowC67 ⋊ C2×#1387

Subgroups

subgroupG/H
centerC22#102×D67
commutatorC8×C67C2×C42
FrattiniC22×C8C22×D67
FittingC67×#1387C2
socleC22×C67C2×#102
prime radicalC23×D67SD16
cosocleC22×C8×C67C23
hypercenter#1387D67
hypocenterC67C2×#1387
LCSG ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

614 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, 84489);