Finite Group Databasebeta

#108×D397 #38762566

order25408
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D397

Splittings

Fitting#108×C397 ⋊ C2
SylowC397 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D397
commutatorC4×C397C22×C4
FrattiniC2×C4C22×D397
Fitting#108×C397C2
socleC2×C397C2×C4⋊C4
prime radicalC22×D397Q8
cosocleC2×C4×C397C23
hypercenter#108D397
hypocenterC397C2×#108
LCSG ▷ C4×C397 ▷ C2×C397 ▷ C397
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6352

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25408, 593);