Finite Group Databasebeta

#101×D409 #39909225

order26176
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#101×D409

Splittings

Fitting#101×C409 ⋊ C2
SylowC409 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D409
commutatorC22×C409C22×C4
FrattiniC2×C4C22×D409
Fitting#101×C409C2
socleC2×C409C2×C22⋊C4
prime radicalC22×D409C2×C4
cosocleC2×C4×C409C23
hypercenter#101D409
hypocenterC409C2×#101
LCSG ▷ C22×C409 ▷ C2×C409 ▷ C409
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6544

Conjugacy classes & character table

2266 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26176, 527);