Finite Group Databasebeta

C2×#22558335 #30770809

order17152
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22558335

Splittings

SylowC67 ⋊ C2×#1394

Subgroups

subgroupG/H
centerC23#14523957
commutatorC2×C4×C67C2×C42
FrattiniC22×Q8C22×D67
FittingC22×#101×C67C2
socleC23×C67#99
prime radicalC24×C67C22⋊C4
cosocleC22×Q8×C67C23
hypercenterC22×#101D67
hypocenterC67C2×#1394
LCSG ▷ C2×C4×C67 ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C24 ◁ C23×Q8 ◁ C22×#101

818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1504 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 84546);