Finite Group Databasebeta

#473×Dic67 #30862723

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#473×Dic67

Splittings

SylowC67 ⋊ C4×#473

Subgroups

subgroupG/H
centerC22#121×D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC2×#473×C67C2
socleC22×C67C2×#121
prime radicalC2×#41×C67C23
cosocleC22×C4×C67C24
hypercenterC2×#473D67
hypocenterC67C4×#473
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#473

882 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

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, 176460);