Finite Group Databasebeta

#108×D53 #16810667

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

Aliases

direct product#108×D53

Splittings

Fitting#108×C53 ⋊ C2
SylowC53 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D53
commutatorC4×C53C22×C4
FrattiniC2×C4C22×D53
Fitting#108×C53C2
socleC2×C53C2×C4⋊C4
prime radicalC22×D53Q8
cosocleC2×C4×C53C23
hypercenter#108D53
hypocenterC53C2×#108
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 848

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, 593);