Finite Group Databasebeta

#41×#11761615 #31737243

order17152
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct product#41×#11761615

Splittings

FittingQ8×#41×C67 ⋊ C2
SylowC67 ⋊ SD16×#41

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingQ8×#41×C67C2
socleC22×C67C23×D4
prime radical#41×D268C2
hypercenterQ8×#41D67
hypocenterC67SD16×#41
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ Q8×#41

2116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1050980);