Finite Group Databasebeta

#41×Dic268 #31737304

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

Aliases

direct product#41×Dic268

Splittings

SylowC67 ⋊ Q16×#41

Subgroups

subgroupG/H
centerC2×C4C22×D268
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC8×#41×C67C2
socleC22×C67C23×D4
prime radicalC2×#41×C67D4
hypercenterC8×#41D67
hypocenterC67Q16×#41
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41

1826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1051041);