Finite Group Databasebeta

#455×Dic71 #32003338

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#455×Dic71

Splittings

SylowC71 ⋊ C4×#455

Subgroups

subgroupG/H
centerC22#120×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#455×C71C2
socleC22×C71C2×#120
prime radicalC2×H(5,𝔽2)×C71C22
cosocleC22×C4×C71C24
hypercenterC2×#455D71
hypocenterC71C4×#455
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#455

1442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 175454);