Finite Group Databasebeta

#101×D523 #45690183

order33472
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#101×D523

Splittings

Fitting#101×C523 ⋊ C2
SylowC523 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D523
commutatorC22×C523C22×C4
FrattiniC2×C4C22×D523
Fitting#101×C523C2
socleC2×C523C2×C22⋊C4
prime radicalC22×D523C2×C4
cosocleC2×C4×C523C23
hypercenter#101D523
hypocenterC523C2×#101
LCSG ▷ C22×C523 ▷ C2×C523 ▷ C523
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8368

Conjugacy classes & character table

2893 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 527);