Finite Group Databasebeta

#435×D167 #36332813

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#435×D167

Splittings

Fitting#435×C167 ⋊ C2
SylowC167 ⋊ C2×#435

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D167
commutator, socleC22×C167C23×C4
Fitting#435×C167C2
prime radicalC2×D4×D167C4
cosocleC2×C4×C167C24
hypercenter#435D167
hypocenterC167C2×#435
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C2×C4 ◁ #435

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5344

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 13185);