Finite Group Databasebeta

#101×D61 #16839740

order3904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#101×D61

Splittings

Fitting#101×C61 ⋊ C2
SylowC61 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D61
commutatorC22×C61C22×C4
FrattiniC2×C4C22×D61
Fitting#101×C61C2
socleC2×C61C2×C22⋊C4
prime radicalC22×D61C2×C4
cosocleC2×C4×C61C23
hypercenter#101D61
hypocenterC61C2×#101
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3904, 527);