Finite Group Databasebeta

#102×#92420 #30597668

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#102×#92420

Splittings

SylowC61 ⋊ C8×#102

Subgroups

subgroupG/H
centerC23D4×#6923
commutatorC4×C61C2×C4×C8
FrattiniC22×C4C22×#6923
FittingC2×#102×C61C4
socleC23×C61C4×D4
prime radicalC22×D4×C61C2×C4
cosocleC2×C4×Dic61C23
hypercenterC2×#102#6923
hypocenterC61C8×#102
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1087223);