Finite Group Databasebeta

#1388×D67 #30770760

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

Aliases

direct product#1388×D67

Splittings

FittingC67×#1388 ⋊ C2
SylowC67 ⋊ C2×#1388

Subgroups

subgroupG/H
centerC4#102×D67
commutatorC8×C67C2×C42
FrattiniC22×C8C22×D67
FittingC67×#1388C2
socleC2×C67C2×#340
prime radicalC23×D67Q16
cosocleC22×C8×C67C23
hypercenter#1388D67
hypocenterC67C2×#1388
LCSG ▷ C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1388

554 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

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, 84497);