Finite Group Databasebeta

#108×D43 #14582943

order2752
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D43

Splittings

Fitting#108×C43 ⋊ C2
SylowC43 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D43
commutatorC4×C43C22×C4
FrattiniC2×C4C22×D43
Fitting#108×C43C2
socleC2×C43C2×C4⋊C4
prime radicalC22×D43Q8
cosocleC2×C4×C43C23
hypercenter#108D43
hypocenterC43C2×#108
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 688

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 593);