Finite Group Databasebeta

#101×D311 #34091672

order19904
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#101×D311

Splittings

Fitting#101×C311 ⋊ C2
SylowC311 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D311
commutatorC22×C311C22×C4
FrattiniC2×C4C22×D311
Fitting#101×C311C2
socleC2×C311C2×C22⋊C4
prime radicalC22×D311C2×C4
cosocleC2×C4×C311C23
hypercenter#101D311
hypocenterC311C2×#101
LCSG ▷ C22×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4976

Conjugacy classes & character table

1727 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19904, 527);