Finite Group Databasebeta

#106×D53 #16810652

order3392
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#106×D53

Splittings

Fitting#106×C53 ⋊ C2
SylowC53 ⋊ C2×#106

Subgroups

subgroupG/H
centerC22D4×D53
commutatorC4×C53C22×C4
FrattiniC2×C4C22×D53
Fitting#106×C53C2
socleC22×C53C2×D4
prime radicalC22×D53D4
cosocleC2×C4×C53C23
hypercenter#106D53
hypocenterC53C2×#106
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1696

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3392, 578);